It has emerged that Foreign Office officials quietly asked the respected National Institute of Economic and Social Research to examine the impact of new European “freedom of movement” rules which from Jan 1, 2014 will potentially allow 29 million Bulgarians and Romanians to live and work in Britain.

Downing Street said the report had only been commissioned two weeks ago. The Prime Minister’s official spokesman said it would be published “in due course”. The Daily Telegraph has established that it was commissioned by officials at the Foreign Office six months ago and that a “draft final version” is now with civil servants.

On Monday night Labour accused the Government of attempting to cover up the potentially embarrassing document.

The report was drawn up by Heather Rolfe, a research fellow at the institute for the past 15 years who has advised the Home Office’s migration advisory committee. She was supported by a team of three colleagues, including the institute’s director Jonathan Portes, a former senior economist in Whitehall.

Mr Portes said: “We are looking at the likely impact of Bulgarian and Romanian immigration post-January 2014, in particular on public services.” Mr Portes declined to comment on the contents of the report but said it was “substantive” and that it was up to the Foreign Office to decide when to publish.

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It was unclear on Monday night whether the report has yet been shown to ministers.

Labour insisted that the report be published. Chris Bryant, the shadow immigration minister, said: “The Government has got to be straight with people – if they have got projections they should publish them.”

A Foreign Office spokesman said: “The Foreign Office commissioned a study by National Institute of Economic and Social Research to evaluate the possible impact of the ending of transitional controls on Romanian and Bulgarian nationals.

“The report does not and was never intended to contain a forecast of numbers relating to Romanian or Bulgarian immigrants.”